Limaçon Evolute

$\begin{figure}\begin{center}\BoxedEPSF{LimaconEvolute.epsf scaled 750}\end{center}\end{figure}$

The Catacaustic of a Circle for a Radiant Point is the limaçon evolute. It has parametric equations

$\displaystyle x$	$\textstyle =$	$\displaystyle {a[4a^2+4b^2+9ab\cos t-ab\cos(3t)]\over 4(2a^2+b^2+3ab\cos t)}$
$\displaystyle y$	$\textstyle =$	$\displaystyle {a^2b\sin^3 t\over 2a^2+b^2+3a b\cos t}.$